The function may be called by the names: f07atc, nag_lapacklin_zgeequ or nag_zgeequ.
f07atc computes the diagonal scaling matrices. The diagonal scaling matrices are chosen to try to make the elements of largest absolute value in each row and column of the matrix given by
have absolute value . The diagonal elements of and are restricted to lie in the safe range , where is the value returned by function X02AMC. Use of these scaling factors is not guaranteed to reduce the condition number of but works well in practice.
1: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – IntegerInput
On entry: , the number of rows of the matrix .
3: – IntegerInput
On entry: , the number of columns of the matrix .
4: – const ComplexInput
Note: the dimension, dim, of the array a
must be at least
The th element of the matrix is stored in
On entry: the matrix whose scaling factors are to be computed.
5: – IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
if , .
6: – doubleOutput
On exit: if NE_NOERROR or NE_MAT_COL_ZERO, r contains the row scale factors, the diagonal elements of . The elements of r will be positive.
7: – doubleOutput
On exit: if NE_NOERROR, c contains the column scale factors, the diagonal elements of . The elements of c will be positive.
8: – double *Output
On exit: if NE_NOERROR or NE_MAT_COL_ZERO, rowcnd contains the ratio of the smallest value of to the largest value of . If and amax is neither too large nor too small, it is not worth scaling by .
9: – double *Output
On exit: if NE_NOERROR, colcnd contains the ratio of the smallest value of to the largest value of .
If , it is not worth scaling by .
10: – double *Output
On exit: . If amax is very close to overflow or underflow, the matrix should be scaled.
11: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
On entry, .
On entry, . Constraint: .
On entry, and .
On entry, and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Column of is exactly zero.
Row of is exactly zero.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The computed scale factors will be close to the exact scale factors.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f07atc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.